Continuous phase modulation for satellite communications

ABSTRACT

A new coded continuous phase modulation (CPM) scheme is proposed to enhance physical layer performance of the current DVB-RCS standard for a satellite communication system. The proposed CPM scheme uses a phase pulse design and combination of modulation parameters to shape the power spectrum of CPM signal in order to improve resilience to adjacent channel interference (ACI). Additionally, it uses a low complexity binary convolutional codes and S-random bit interleaving. Phase response using the proposed CPM scheme is a weighted average of the conventional rectangular and raised-cosine responses and provides optimum response to minimize frame error rate for a given data rate.

The present application claims priority from U.S. ProvisionalApplication No. 61/331,078 filed May 14, 2010, the entire disclosure ofwhich is incorporated herein by reference.

BACKGROUND

The present invention relates to satellite communication systems,non-limiting examples of which include Digital Video Broadcasting (DVB)and the physical layer performance of the current DVB-RCS (Digital VideoBroadcasting-Return Channel Satellite) standard for satellitecommunication systems.

In multi-access wireless communication systems, for example, FrequencyDivision Multiple Access (FDMA) systems, multiple users share theavailable system resources. A problem in systems where the communicationchannel is shared by several users is spectral spreading, wherein onechannel “bleeds over” into another channel, which is referred to asAdjacent Channel Interference (ACI). This ACI problem can cause seriousperformance degradation. This is because in order to achieve highbandwidth/spectral efficiencies, the frequency separation between theadjacent channels (carriers) must be reduced, causing an increase in ACIand resulting in performance degradation.

The performance of such systems can be improved through a more judiciouschoice of the modulation and channel (error correction) coding in thephysical layer function of the system. Continuous phase modulation is aknown method to modulate the data in communication systems. Continuousphase modulator (CPM) modulates the carrier phase in a continuous mannerand is known to improve spectral efficiency and power efficiency of thedata signal.

Operation of a transmitter and a receiver for a satellite communicationsystem using continuous phase modulation is described below.

FIG. 1 illustrates a prior art transmitter 100 for a conventionalsatellite communication system.

As illustrated in FIG. 1, transmitter 100, which may transmit over achannel 112 includes a bit source 102, a binary convolutional coder 104,a S-random interleaver 106, a bit-to-symbol generator 108 and a CPM 110.In this illustration, each of bit source 102, binary convolutional coder104, S-random interleaver 106, bit-to-symbol generator 108, CPM 110 andchannel 112 are illustrated as distinct devices. However, at least twoof bit source 102, binary convolutional coder 104, S-random interleaver106, bit-to-symbol generator 108 and CPM 110 may be combined as aunitary device.

Bit source 102 is arranged to provide a data bits signal 114 to binaryconvolutional coder 104. Binary convolutional coder 104 is arranged toreceive data bits signal 114 from bit source 102 and provide an encodeddata bits 116 to S-random interleaver 106. S-random interleaver 106 isarranged to receive encoded data bits 116 from binary convolutionalcoder 104 and provide a scrambled data bits 118 to bit-to-symbolgenerator 108. Bit-to-symbol generator 108 is arranged to receivescrambled data bits 118 from S-random interleaver 106 and provide a datasymbols signal 120 to CPM 110. CPM 110 is arranged to receive datasymbols signal 120 from bit-to-symbol generator 108 and provide amodulated waveform signal 122 to channel 112. Channel 112 is arranged toreceive modulated waveform 122 from CPM 110 and provide a channel output124.

Bit source 102 is operable to provide data bits signal 114 to betransmitted through channel 112. Non-limiting examples for bit source102 include data, images, video, audio, etc.

Binary convolutional coder 104 is operable to encode data bits signal114 using a convolutional code and provides forward error correction ondata bits 114. Non-limiting examples of convolutional coding includerecursive and non-recursive, systematic and non-systematic convolutionalcodes. Purpose of forward error correction (FEC) is to improve thecapacity of a channel by adding some carefully designed redundantinformation to the data being transmitted through the channel. Binaryconvolution coding is a form of channel coding to add this redundantinformation to the data.

S-random interleaver 106 is operable to scramble the encoded data bits116 by rearranging the bit sequence in order to improve error rateperformance and lower the error floors. Interleaving is a process ofrearranging the ordering of a data sequence in a one to onedeterministic format. The inverse of this process is callingdeinterleaving, which restores the received sequence to its originalorder. Interleaving is used to enhance the error correcting capabilityof coding. An S-random interleaver (where S=1, 2, 3 . . . ) is a“semi-random” interleaver, which changes the order of the data sequenceof incoming input symbols, and generally provides the permuted datasequence in the form of an interleaving matrix.

Bit-to-symbol generator 108 is operable to convert the scrambled databits 118 to data symbols signal 120 in preparation for modulation. CPM110 is operable to modulate data symbols signal 120 using a modulationscheme. Non-limiting examples of modulation schemes provided by CPM 100include minimum shift keying (MSK) and Gaussian minimum shift keying(GMSK). Modulated data symbols signal 122 is transmitted to externalentities (not shown) via channel output 124. Channel output 124 may beconsidered as part of the external entities.

FIG. 2 illustrates a prior art receiver 200 for a conventional satellitecommunication system.

As illustrated in FIG. 2, receiver 200 includes a CPM correlator bank202, a CPM detector 204, a S-random deinterleaver 206, a binaryconvolutional decoder 208, and a S-random interleaver 210. In thisillustration, each of CPM correlator bank 202, CPM detector 204,S-random deinterleaver 206, binary convolutional decoder 208, andS-random interleaver 210 are illustrated as distinct devices. However,at least two of CPM correlator bank 202, CPM detector 204, S-randomdeinterleaver 206, binary convolutional decoder 208, and S-randominterleaver 210 may be combined as a unitary device.

CPM correlator bank 202 is arranged to receive channel output 212 from atransmitting source, for example, channel output 124 from transmitter100. CPM detector 204 is arranged to receive statistical estimates ofall possible transmitted CPM waveforms 214 from CPM correlator bank 202and scrambled estimates of the probability that the transmitted codebits(i.e. bits generated by the convolutional code) are either a 1 or 0 fromS-random interleaver 210 and output probability estimates of thetransmitted symbols as a detected signal 216 to S-random deinterleaver206. S-random deinterleaver 206 is arranged to receive the updatedprobability estimates of the transmitted symbols as detected signal 216from CPM detector 204 and output descrambled probability estimates ofthe transmitted codebits as a descrambled signal 218 to binaryconvolutional decoder 208. Binary convolutional decoder 208 is arrangedto receive descrambled signal 218 from S-random deinterleaver 206 andoutput a bit sequence 220 to external entities (not shown) and codebitprobabilities as decoded signal 222 to S-random interleaver 210.S-random interleaver 210 is arranged to receive decoded signal 222 frombinary convolutional decoder 208 and output scrambled codebitprobabilities as a signal 224 to CPM detector 204.

CPM correlator bank 202 operates to receive channel output 212 from atransmitting source, for example transmitter 100. CPM correlator bank202 may operate to correlate the received signal with N possibletransmitted signals, where N is a finite integer number and depends onthe specific choice of CPM modulation parameters. CPM correlator bankfunctions as a matched filter and provides a matrix indicating howclosely related the received signal may be to each of those N possibletransmitted signals. Correlated signal 214 provides a statisticalindication as to which one of N possible transmitted signals may be thereceived signal.

CPM detector 204 is operable to use the statistics provided bycorrelated signal 214 to perform decoding of a received signal forproviding an estimate of the received symbols. Non-limiting examples ofdecoding algorithms performed by CPM detector 204 includes Viterbi,BCJR, etc. CPM detector 204 may also operate to receive scrambledprobabilities of the transmitted codebits being either a 1 or a 0 (i.e.bits generated by the convolutional code) as signal 224 from S-randominterleaver 210 in order to provide a better estimate of the receivedsignal.

Every interleaver has a corresponding deinterleaver, which acts on theinterleaved data sequence and restores it to its original order. Thede-interleaving matrix is generally the transpose of the interleavingmatrix. S-random deinterleaver 206 is operable to descramble thedetected signal 216 from CPM detector 204. S-random deinterleaver 206operates to provide the descrambled signal 218 to binary convolutionaldecoder 208.

Binary convolutional decoder 208 may operate to use a decoding algorithmto decode using descrambled probabilities from descrambled signal 218for providing a decoded signal 222 and bit sequence 220. Non-limitingexamples of decoding algorithms include Viterbi, BCJR, etc.

S-random interleaver 210 is operable to improve the error rateperformance by feeding the scrambled signal 224 back to CPM detector204. The goal of receiver 200 is to recover the received signal suchthat bit sequence 220 recovered by receiver 200 matches the bit sequenceprovided by the transmitting source.

The first pass through CPM detector 204, S-random deinterleaver 206 andbinary convolutional decoder 208 provides an estimate of bit sequence220 which may match with the transmitted bit source. The operation ofS-random interleaver 210 providing feedback to CPM detector 204 improvesthe signal estimate with successive iterations though the feedback loop,until recovered information matches information provided by thetransmitting source or until a maximum number of iterations areperformed, whichever occurs first.

The operation of a conventional transmitter, which involved encoding,scrambling and modulation of a bit source for transmission via a channelof a communication system was discussed previously with respect toFIG. 1. The operation of a conventional receiver, which involvedcorrelating, descrambling and decoding of the received bit source fromthe channel to recover the original bit source, was discussed withrespect to FIG. 2.

In communication systems, ACI can seriously impair performance,especially when high bandwidth efficiencies are desired. In order toachieve high bandwidth/spectral efficiencies, the frequency separationbetween the adjacent channels (carriers) must be reduced, causing anincrease in ACI and resulting in performance degradation. A commonpractice to improve the performance is by applying interferencecancellation at the receiver however, this entails a significantincrease in the complexity.

Alternatively, the performance could also be improved using a continuousphase modulation scheme with a more judicious choice of the modulationand channel (error correction). Through the design of the CPM phasepulse and selection of the remaining modulation parameters, powerspectrum of the CPM signal can be shaped to improve the resilience toACI.

Additionally, with the continuous phase modulation schemes used byconventional CPMs, error rate performance for information flow between atransmitter and a receiver for a satellite communication system does notprovide optimum results in recovering the bit source at the receiver ascompared to the transmitted bit source.

What is needed is an improved CPM scheme for communication systems forincreasing error rate performance of information flow. An improved CPMscheme should provide an improved resilience to adjacent channelinterference and also improve error rate performance for both high andlow frame error rates.

BRIEF SUMMARY

Embodiments of the present invention may operate to provide a CPM schemeexhibiting an improved resilience to adjacent channel interference andalso provide an improved error rate performance at both high and lowframe error rates using low complexity binary convolutional codes andS-random bit interleaving, and in particular may operate to enhance thephysical layer performance of the current DVB-RCS standard for asatellite communication system or any satellite communications system ingeneral.

In accordance with an aspect of the present invention, a device for usewith a bit source, which can provide a source data stream. The deviceincludes a bit-to-symbol generator and a continuous phase modulator. Thebit-to-symbol generator can output a symbol stream of a plurality ofdifferent types of symbols, wherein the symbol stream is based on thesource data stream. The continuous phase modulator can output amodulated signal based on the symbol stream. The modulated signal isbased on an alphabet size of the plurality of different types ofsymbols, a modulation index h, a pulse shape and a pulse width: whereinq_(av) is a continuous phase modulation phase response of a pulse shapefor the modulator as a function of time; wherein q_(rc) is a continuousphase modulation phase response of raised-cosine-shaped pulses as afunction of time; wherein q_(re) is a continuous phase modulation phaseresponse of rectangular-shaped pulses as a function of time, and whereinq_(av) is a linear function of q_(rc) and q_(re).

Additional advantages and novel features of the invention are set forthin part in the description which follows, and in part will becomeapparent to those skilled in the art upon examination of the followingor may be learned by practice of the invention. The advantages of theinvention may be realized and attained by means of the instrumentalitiesand combinations particularly pointed out in the appended claims.

BRIEF SUMMARY OF THE DRAWINGS

The accompanying drawings, which are incorporated in and form a part ofthe specification, illustrate an exemplary embodiment of the presentinvention and, together with the description, serve to explain theprinciples of the invention. In the drawings:

FIG. 1 illustrates a prior art transmitter for a conventional satellitecommunication system;

FIG. 2 illustrates a prior art receiver for a conventional satellitecommunication system;

FIG. 3 illustrates an example transmitter, in accordance with aspects ofthe present invention;

FIG. 4 illustrates an example receiver, in accordance with aspects ofthe present invention;

FIG. 5 illustrates a graph of CPM phase response with time, inaccordance with aspects of the present invention;

FIG. 6 illustrates a graph of frame error rate (FER) with signal tonoise ratio for center carrier at 0.5 b/s/Hz, in accordance with aspectsof the present invention;

FIG. 7 illustrates a graph of frame error rate (FER) with signal tonoise ratio for center carrier at 0.75 b/s/Hz, in accordance withaspects of the present invention;

FIG. 8 illustrates a graph of frame error rate (FER) with signal tonoise ratio for center carrier at 1.1 b/s/Hz, in accordance with aspectsof the present invention;

FIG. 9 illustrates a graph of frame error rate (FER) with signal tonoise ratio for center carrier at 1.25 b/s/Hz, in accordance withaspects of the present invention;

FIG. 10 illustrates a graph of frame error rate (FER) with signal tonoise ratio for center carrier at 1.5 b/s/Hz, in accordance with aspectsof the present invention; and

FIG. 11 illustrates a graph of frame error rate (FER) with signal tonoise ratio for center carrier at 1.8 b/s/Hz, in accordance with aspectsof the present invention.

DETAILED DESCRIPTION

Embodiments of the present invention may operate to provide a coded CPMscheme for a wireless communication system as described below. Throughthe design of the CPM phase pulse and selection of the remainingmodulation parameters, the power spectrum can be shaped to improve theresilience with respect to ACI. Additionally, the coded CPM scheme mayoperate to enhance the physical layer performance of the current DVB-RCSstandard for satellite communication systems by improving error rateperformance for both high and low frame error rates using low-complexitybinary convolutional codes and S-random bit interleaving.

FIG. 3 illustrates an example transmitter 300, in accordance with anaspect of the present invention.

Transmitter 300 includes some elements of transmitter 100 of FIG. 1,mainly, bit source 102, binary convolutional coder 104, S-randominterleaver 106, bit-to-symbol generator 108 and channel 112. In placeof CPM 110 of transmitter 100, transmitter 300 includes a CPM 302.

As illustrated in FIG. 3, each of bit source 102, binary convolutionalcoder 104, S-random interleaver 106, bit-to-symbol generator 108, CPM302 and channel 112 are illustrated as distinct devices. However, atleast two of bit source 102, binary convolutional coder 104, S-randominterleaver 106, bit-to-symbol generator 108 and CPM 302 may be combinedas a unitary device.

Bit-to-symbol generator 108 is arranged to receive scrambled data bits118 from S-random interleaver 106 and provide data symbols signal 120 toCPM 302. CPM 302 is arranged to receive data symbols signal 120 frombit-to-symbol generator 108 and provide a modulated data symbols signal304 to channel 112. Channel 112 is arranged to receive modulated datasymbols signal 304 from CPM 302 and provide channel output 124.

Bit source 102, binary convolutional coder 104, S-random interleaver106, bit-to-symbol generator 108 and channel 112 operate as describedpreviously for transmitter 100 with reference to FIG. 1. CPM 302 mayoperate in accordance with modulator code parameters as described inmore detail in the following discussion.

Operation of transmitter 300 will be explained below in detail for avector of information bits u, provided as data bits signal 114 from bitsource 102:u=[u ₀ , u ₁ , . . . , u _(N) _(u) −1]ε{0,1},which may be encoded by binary convolutional coder 104 to produceencoded data bits 116 with codewordb′=[b′ ₀ ,b′ ₁ , . . . , b′ _(N) _(b) ⁻¹]ε{0,1}.The code rate for binary convolutional coder 104 may be calculated as

$R_{c} = {\frac{N_{u}}{N_{b}}.}$

Output of binary convolutional coder 104 may be bit interleaved byS-random interleaver 106 to produce scrambled data bits 118 asinterleaved codewordb=[b ₀ , b ₁ , . . . , b _(N) _(b) ⁻¹].

The interleaved codeword may be arranged in a log₂ M×N_(s) matrix B withthe (i, k) element given byB _(ik) =b _(k log) ₂ _(M+i).Each column of B may be mapped to one of M symbols by bit-to-symbolgenerator 108 to produce data symbols 120 as vector

${a = {\left\lbrack {a_{0},a_{1},\ldots\mspace{14mu},a_{N_{s} - 1}} \right\rbrack \in \left\{ {0,1,\ldots\mspace{14mu},{M - 1}} \right\}}};{N_{s} = {\frac{N_{b}}{\log_{2}M}.}}$

A symbol sequence may be provided to CPM 302. An Alphabet with size ofM=4 and a modulation influenced bit-to-symbol mapping is discussed. Morespecifically, when the modulation index h=m/p has p=2 or 3, followingmapping scheme may be used:

Bits Symbol 00 0 01 1 10 2 11 3else the following mapping scheme may be used:

Bits Symbol 00 0 01 1 11 2 10 3

The modulated CPM signal 304 can be represented using one of manypossible methods, such as (but not limited to) Rimoldi's decompositionapproach, or in terms of Laurent pulses. For purposes of discussion,Rimoldi's decomposition approach is followed in order to representmodulated CPM signal 304. Rimoldi's decomposition approach allowsdescribing any CPM signal with a rational modulation index using afinite-state machine with a time-invariant trellis. Channel 112 may bemodeled as zero-mean Additive White Gaussian Noise (AWGN).

As described previously with respect to FIG. 3, operation of transmitter300 was discussed using CPM 302 in accordance with aspects of thepresent invention. Performance of CPM 302 with proposed modulator codeparameters will be described in more detail below with reference toFIGS. 5-11.

FIG. 4 illustrates an example receiver 400, in accordance with aspectsof the present invention.

Receiver 400 includes some elements of receiver 200 of FIG. 2, mainly,CPM detector 204, S-random deinterleaver 206, binary convolutionaldecoder 208, and S-random interleaver 210. In place of CPM correlatorbank 202 of receiver 200, receiver 400 includes a CPM correlator bank402.

As illustrated in FIG. 4, each of CPM correlator bank 402, CPM detector204, S-random deinterleaver 206, binary convolutional decoder 208, andS-random interleaver 210 are illustrated as distinct devices. However,at least two of CPM correlator bank 402, CPM detector 204, S-randomdeinterleaver 206, binary convolutional decoder 208, and S-randominterleaver 210 may be combined as a unitary device.

CPM correlator bank 402 is arranged to receive channel output 212 andoutput a correlated signal 404 to CPM detector 204.

CPM detector 204, S-random deinterleaver 206, binary convolutionaldecoder 208, and S-random interleaver 210 operate as described above forreceiver 200 with reference to FIG. 2.

CPM detector 204 follows soft-in soft-out (SISO) methodology. CPMdetector 204 generates maximum a posteriori (MAP) probabilities for thetransmitted bit source by executing BCJR algorithm on the time-invarianttrellis describing the modulation.

Binary convolutional decoder 208 also performs SISO detection byexecuting the BCJR algorithm on the trellis describing the convolutionalcode. For the binary convolutional decoder 208, the constraint length 3code decodes on a 4 state trellis, whereas the constraint length 4 coderequires an 8 state trellis. In order to improve the signal estimate,information is exchanged between CPM detector 204 and binaryconvolutional decoder 208 during successive iterations until recoveredinformation matches information provided by the transmitting source.

The coded system performance is evaluated at the following six spectralefficiencies: 0.5 b/s/Hz, 0.75 b/s/Hz, 1.1 b/s/Hz, 1.25 b/s/Hz, 1.5b/s/Hz and 1.8 b/s/Hz. For the analysis, it was assumed the CPM signalshares the AWGN channel with 4 interfering, equally spaced, carriers(i.e. two carriers on either side of the desired carrier). If f_(i) andf_(j) are the center frequencies for the i^(th) and j^(th) carriers,then the frequency separation between two immediate neighbors is,Δ_(f) =|f _(i) −f _(j)|, for all, |i−j|=1.

The spectral efficiency may be measured as,

${\eta = \frac{R_{c}\log_{2}M}{\Delta_{f}T}},$where T is the symbol duration.

For the analysis, it was assumed that the carriers are homogenous, i.e.they all use the same CPM modulation parameters.

As discussed previously with respect to FIG. 4, CPM 302 and CPMcorrelator bank 402 operate in accordance with an aspect of the presentinvention for providing a phase response generating an improved FER.Performance of CPM 302 and CPM correlator bank 402 in addition toproposed modulator code parameters will be described in more detail inthe following discussion with reference to FIGS. 5-11.

FIG. 5 illustrates a graph 500 of CPM phase response with time, inaccordance with aspects of the present invention.

As illustrated in the figure, an y-axis 502 represents the CPM phaseresponse in radians and a x-axis 504 represents the time normalized bysymbol duration or time multiplied by symbol rate (t/T). CPM phaseresponse is represented by a function q(t). Graph 500 includes a curve506 which represents the phase response for a rectangular CPM(q_(RE)(t)) and a curve 508 which represents the phase response for araised-cosine CPM (q_(RC)(t)). Graph 500 also includes a curve 510 inaccordance with an aspect of the present invention, which represents theaverage phase response (q_(AV)(t)) calculated as:q _(AV)(t)=α_(RE) *q _(RE)(t)+α_(RC) *q _(RC)(t),where α_(RE)=0.25 and α_(RC)=0.75 for graph 500. Values of α_(RE) andα_(RC) may be programmable in order to achieve a particular phaseresponse.

Function q(t) shapes power spectrum density at the modulator. Each ofcurves 506, 508 and 510 provide a different power spectrum. Curves 506and 508 are responses from a conventional CPM, such as CPM 110 asdescribed with reference to FIG. 1.

Curve 506 illustrates the phase response of a CPM signal having withpower spectrum having a narrow main lobe but very large spectrum sidelobes. Curve 508 illustrates the phase response of a CPM signal yieldinga power spectrum which has very small spectral side lobes but very largemain lobe. The proposed phase response, in accordance with an aspect ofthe present invention, may be illustrated as curve 510, which may berepresented as a weighted average of the responses of curves 506 and508, as described previously with the function q_(AV)(t). Curve 510illustrates the phase response of a CPM signal whose spectral main lobesand side lobes can be shaped to improve resilience to ACI. CPM 302 andCPM correlator bank 402 may operate, in accordance with an aspect of thepresent invention, in order to provide a phase response using functionq_(AV)(t) resulting in an improved FER.

CPM 302 and CPM correlator bank 402 may operate in accordance withproposed modulator code parameters as described below with reference toTable 1:

TABLE 1 Al- pha- Modu- bet lation Pulse b/s/ size index Pulse shape CodeHz M h width AV FEC Rate Δ_(f)T 0.5 4 2/5 2 α_(RE) = 0.02 (5, 7)_(octal)1/2 2.0 α_(RC) = 0.98 0.75 4 1/3 2 α_(RE) = 0.25 (5, 7)_(octal) 1/21.333 α_(RC) = 0.75 1.1 4 2/7 2 α_(RE) = 0.25 (5, 7)_(octal) 2/3 1.21α_(RC) = 0.75 1.25 4 2/7 2 α_(RE) = 0.25 (5, 7)_(octal) 2/3 1.067 α_(RC)= 0.75 1.5 4 1/4 2 α_(RE) = 0.25 (15, 17)_(octal) 4/5 1.0667 α_(RC) =0.75 1.8 4 1/5 2 α_(RE) = 0.35 (15, 17)_(octal) 6/7 0.974 α_(RC) = 0.65

As illustrated in Table 1, column 1 displays “b/s/Hz”, which indicatestransmission rate as bits/sec/Hertz. Typically, as the rate oftransmission increases, the amount of energy required also increases.

Column 2 displays “Alphabet size M,” which indicates the maximum numberof different symbols that may be transmitted. Consider for example asituation where the alphabet size is two, wherein a symbol may betransmitted on one of two positions on a circular circumference, e.g.,the 12:00 position of a clock and the 6:00 position of a clock. In thisexample situation, suppose the transmitted symbol lies on the 12:00position of a clock and the corresponding received symbol lies on the2:00 position of a clock. In such a case, the receiver will likely beable to correctly determine that the transmitted symbol was on the 12:00position of a clock. Clearly, when the alphabet size is two, the amountof data/symbol is limited to one of two, but the likelihood ofdetermining the correctly transmitted symbol is relatively large.

Now consider the example situation where the alphabet size is 4, whereina symbol may be transmitted on one of four positions on a circularcircumference, e.g., the 12:00, the 3:00, the 6:00 and the 9:00positions on a clock. In this example situation, suppose the transmittedsymbol lies on the 12:00 position of a clock, but the received symbollies on the 2:00 position of a clock. In such a case, the receiver mayincorrectly determine that the transmitted symbol was located on the3:00 position of a clock. Clearly, when the alphabet size is four, theamount of data/symbol is limited to one of four or twice that in thesituation where the alphabet size is two, but the likelihood ofdetermining the correctly transmitted symbol is much smaller than thesituation where the alphabet size is two. Generally, as the alphabetsize increases, the amount of data that can be transmitted per symbolincreases and the probability of incorrectly determining a transmittedsymbol also increases.

Column 3 displays “Modulation index h,” wherein h is a parameter thatshapes the power spectrum in CPM 302 and CPM correlator bank 402.Further, h also affects the frame error rate performance of CPM. Inparticular, in a single-carrier system (i.e. when there are no othercarriers sharing the channel), a larger h is desirable because itresults in an improved error rate performance. However, a larger h alsoresults in the CPM signal having a wider power spectrum. Hence in thepresence of adjacent carrier interference, there is a trade-off betweenthe performance improvement from choosing a larger h and the performancedegradation resulting from the increase in ACI caused by the wider powerspectrum due to a large h.

Column 4 displays “Pulse width in symbol duration”. In particular, thepulse width in each of the entries of Table 1 is “2,” indicating thepulse width is limited to a two-symbol duration, i.e., the duration ittakes to transmit two symbols.

Column 5 displays “Pulse Shape.” The shape in each of the entries ofTable 1 is AV, which corresponds to a linear combination of araised-cosine pulse shape and a rectangular pulse shape, in accordancewith an aspect of the present invention.

Column 6 displays forward error correction or “FEC”. The (5,7)_(octal)entries indicate a 4-state correction, whereas the (15, 17)_(octal)entries indicate an 8 state correction.

Column 7 displays “Code Rate”, which indicates redundancy in thetransmitted code. For example, a code rate of 1/2 implies for everyinformation bit entering the convolutional code, the convolutional codegenerated two codebits. Similarly, a code rate of 2/3 implies that forevery two information bits entering the convolutional code, theconvolutional code generated 3 codebits. The higher the redundancy (i.e.lower the code rate), the higher the probability that the informationbit with be received without error. However, the higher the redundancy,lower the achievable spectral efficiency.

Column 7 displays “Δ_(f)T”, which indicates carrier spacing infrequency. As the carrier spacing decreases, more streams may be placedon a channel. However, as the carrier spacing decreases, ACI increases,thus increasing the probability of error for a received symbol.

Different rows in Table 1 indicate the potentially optimum combinationof parameters listed in column 2 through column 7 for a particulartransmission and reception rate in column 1. The proposed CPM schemeusing the parameters listed in Table 1 provide improved signal to noiseratio for a given frame error rate. For example, for transmitting andreceiving at a rate of 1.1 b/s/Hz, and using: an alphabet size of 4symbols; a modulation index h of 2/7; a pulse width of 2 and pulse shapebased on a AV q function in accordance with an aspect of the presentinvention; an FEC of (5,7)_(octal); a code rate of 2/3 and a carrierspacing of 1.21 may operate to minimize transmission error andconcurrently minimize transmission power. Of course any of theparameters from columns 2-7 of Table 1, within the row corresponding toa transmission rate of 1.1 may be modified. However, such a change mayoperate to increase the transmission error and/or increase the requiredtransmission power needed in order to maintain the desired transmissionand reception rate.

Frame error rates for code and modulation parameters in accordance withan aspect of the present invention listed in Table 1 will now describedfurther with respect to FIGS. 6-11. For the simulation analysis, it wasassumed that all interfering carriers are 3 dB stronger than the centercarrier. For the simulation analysis, a maximum of 30 iterations wereperformed for operation with respect to the CPM detector 204 and binaryconvolutional decoder 208.

As shown in row 1 of Table 1, for a 0.5 b/s/Hz, alphabet size requiredis 4 symbols. Modulation index h is configured to 2/5. Pulse width spans2 symbol duration and pulse shape based on an AV q function inaccordance with an aspect of the present invention; FEC is (5,7)_(octal) is configured indicating a 4 state convolutional code. Coderate is configured for 1/2. Δ_(f)T is configured for 2.0.

FIG. 6 illustrates a graph 600 of FER with signal to noise ratioE_(b)/N₀ for center carrier at 0.5 b/s/Hz, in accordance with aspects ofthe present invention.

As illustrated in the figure, an y-axis 602 represents the FER forcenter carrier (logarithmic scale wherein the error rate does not have aunit) and a x-axis 604 represents the signal to noise ratio orenergy/information bit E_(b)/N₀ (logarithmic scale in dB). Graph 600includes a curve 606.

Graph 600 illustrates the FER performance using the rate 1/2 binaryconvolutional code with generators (5,7)_(octal) in AWGN for the centercarrier at 0.5 b/s/Hz. The length of the information sequence isN_(u)=1504 bits. The modulation parameters are configured as M=4, h=2/5and 2 AV. The multicarrier model assumes a total of four interferingcarriers with +3 dB ACI and Δ_(f)T=2.0.

As shown in FIG. 6, curve 606 represents spectral efficiency for datarate of 0.5 b/s/Hz. Curve 606 indicates that signal to noise ratioincreases with lower frame error rates. The FER performance versussignal to noise ratio E_(b)/N₀ for higher data rates will be discussedfurther.

As shown in row 2 of Table 1, for a 0.75 b/s/Hz rate, alphabet sizerequired is 4 symbols. Modulation index h is configured to 1/3; a pulsewidth of 2 symbol duration and pulse shape based on a AV q function inaccordance with an aspect of the present invention; FEC is (5,7)_(octal)is configured indicating a 4 state convolutional code. Code rate isconfigured for 1/2. Δ_(f)T is configured for 1.333.

FIG. 7 illustrates a graph 700 of FER with signal to noise ratioE_(b)/N₀ for center carrier at 0.75 b/s/Hz, in accordance with aspectsof the present invention.

As illustrated in the figure, an y-axis 702 represents the FER forcenter carrier (logarithmic scale wherein the error rate does not have aunit) and a x-axis 704 represents the signal to noise ratio orenergy/information bit E_(b)/N₀(logarithmic scale in dB). Graph 700includes a curve 706.

Graph 700 illustrates the FER performance using the rate 1/2 binaryconvolutional code with generators (5,7)_(octal) in AWGN for the centercarrier at 0.75 b/s/Hz. The length of the information sequence isN_(u)=1504 bits. The modulation parameters are configured as M=4, h=1/3and 2 AV. The multicarrier model assumes a total of four interferingcarriers with +3 dB ACI and Δ_(f)T=1.333.

As shown in FIG. 7, curve 706 represents spectral efficiency for datarate of 0.75 b/s/Hz. Curve 706 indicates that signal to noise ratioincreases with lower frame error rates. The FER performance versussignal to noise ratio E_(b)/N₀ for higher data rates will be discussedfurther.

As shown in row 3 of Table 1, for a 1.1 b/s/Hz rate, alphabet sizerequired is 4 symbols. Modulation index h is configured to 2/7. A pulsewidth of 2 symbol duration and pulse shape based on a AV q function inaccordance with an aspect of the present invention; FEC is (5,7)_(octal), is configured indicating a 4 state convolutional code. Coderate is configured for 2/3. Δ_(f)T is configured for 1.21. FERperformance versus E_(b)/N₀ of CPM 302 using the parameters of row 2 ofTable 1 is shown in FIG. 7.

FIG. 8 illustrates a graph 800 of FER with signal to noise ratioE_(b)/N₀ for center carrier at 1.1 b/s/Hz, in accordance with aspects ofthe present invention.

As illustrated in the figure, an y-axis 802 represents the FER forcenter carrier (logarithmic scale) and a x-axis 804 represents thesignal to noise ratio or energy/information bit E_(b)/N₀ (logarithmicscale in dB). Graph 800 includes a curve 806.

Graph 800 shows the FER performance using the rate 2/3 binaryconvolutional code with generators (5,7)_(octal) in AWGN for the centercarrier at 1.1 b/s/Hz. The length of the information sequence isN_(u)=1504 bits. The modulation parameters are M=4, h=2/7 and 2 AV. Themulticarrier model assumes a total of four interfering carriers with +3dB ACI and Δ_(f)T=1.21.

As shown in FIG. 8, curve 806 represents spectral efficiency for datarate of 1.1 b/s/Hz. Curve 806 indicates that signal to noise ratioincreases with lower frame error rates. The FER performance versussignal to noise ratio E_(b)/N₀ for higher data rates will be discussedfurther.

As shown in row 4 of Table 1, for a 1.25 b/s/Hz rate, alphabet sizerequired is 4 symbols. Modulation index h is configured to 2/7. A pulsewidth of 2 symbol duration and pulse shape based on a AV q function inaccordance with an aspect of the present invention. FEC is (5,7)_(octal), is configured indicating a 4 state convolutional code. Coderate is configured for 2/3. Δ_(f)T is configured for 1.067. FERperformance versus E_(b)/N₀ of CPM 302 for these parameters is shown inFIG. 9.

FIG. 9 illustrates a graph 900 of FER with signal to noise ratioE_(b)/N₀ for center carrier at 1.25 b/s/Hz, in accordance with aspectsof the present invention.

As illustrated in the figure, an y-axis 902 represents the FER forcenter carrier (logarithmic scale) and a x-axis 904 represents thesignal to noise ratio or energy/information bit E_(b)/N₀ (logarithmicscale in dB). Graph 900 includes a curve 906.

Graph 900 shows the FER performance using the rate 2/3 binaryconvolutional code with generators (5,7)_(octal) in AWGN for the centercarrier at 1.25 b/s/Hz. The length of the information sequence isN_(u)=1504 bits. The modulation parameters are M=4, h=2/7, 2 AV. Themulticarrier model assumes a total of four interfering carriers with +3dB ACI and Δ_(f)T=1.067.

As shown in FIG. 9, curve 906 represents spectral efficiency for datarate of 1.25 b/s/Hz. Curve 906 indicates that signal to noise ratioincreases with lower frame error rates. The FER performance versussignal to noise ratio E_(b)/N₀ for even higher data rate will bediscussed further.

As shown in row 5 of Table 1, for a 1.5 b/s/Hz rate, alphabet sizerequired is 4 symbols. Modulation index h is configured to 1/4. A pulsewidth of 2 symbol duration and pulse shape based on an AV q function inaccordance with an aspect of the present invention. FEC is (15,17)_(octal), is configured indicating a 8 state convolutional code. Coderate is configured for 4/5. Δ_(f)T is configured for 1.0667. FERperformance versus E_(b)/N₀ of CPM 302 for these parameters is shownFIG. 10.

FIG. 10 illustrates a graph 1000 of FER with signal to noise ratioE_(b)/N₀ for center carrier at 1.5 b/s/Hz, in accordance with aspects ofthe present invention.

As illustrated in the figure, an y-axis 1002 represents the FER forcenter carrier (logarithmic scale) and a x-axis 1004 represents thesignal to noise ratio or energy/information bit E_(b)/N₀ (logarithmicscale in dB). Graph 1000 includes a curve 1006.

Graph 1000 shows the FER performance using the 4/5 binary convolutionalcode with generators (15,17)_(octal) in AWGN for the center carrier at1.5 b/s/Hz. The length of the information sequence is N_(u)=1504 bits.The modulation parameters are M=4, h=1/4, 2 AV. The multicarrier modelassumes a total of four interfering carriers with +3 dB ACI andΔ_(f)T=1.0667. Curve 1006 indicates that signal to noise ratio increaseswith lower frame error rates.

FIG. 11 illustrates a graph 1100 of FER with signal to noise ratioE_(b)/N₀ for center carrier at 1.8 b/s/Hz, in accordance with aspects ofthe present invention.

As illustrated in the figure, an y-axis 1102 represents the FER forcenter carrier (logarithmic scale) and a x-axis 1104 represents thesignal to noise ratio or energy/information bit E_(b)/N₀ (logarithmicscale in dB). Graph 1100 includes a curve 1106.

FIGS. 3-4 illustrate transmitter 300 and receiver 400 using proposed CPMscheme, in accordance with aspects of the present invention. Asillustrated in FIG. 5, CPM phase response was calculated and wasrepresented by function q_(AV). The proposed phase response q_(AV),which may be represented as a weighted average of the rectangular andraised-cosine responses, may operate to provide an optimum response forminimizing FER for a given data rate, for example, as shown in Table 1.A CPM scheme, in accordance with aspects of the present invention, usingthe parameters listed in Table 1 may operate to provide improved signalto noise ratio for a given frame error rate. Also, FER for centercarrier was shown with respect to E_(b)/N₀ using the CPM scheme, inaccordance with aspects of the present invention, at example data ratesof 0.5 b/s/Hz 0.75 b/s/Hz, 1.1 b/s/Hz, 1.25 b/s/Hz and 1.5 b/s/Hz and1.8 b/s/Hz. It should be noted that other data rates may be used inaccordance with aspects of the present invention. A data rate, orspectral efficiency, may be chosen based,

${\eta = \frac{R_{c}\log_{2}M}{\Delta_{f}T}},$where Δ_(f)T, the code rate R_(c) and the alphabet size M are provided.In the discussion, it was illustrated from the graphs that for a givenFER, signal to noise ratio increased at higher data rates, in accordancewith aspects of the present invention.

The foregoing description of various preferred embodiments of theinvention have been presented for purposes of illustration anddescription. It is not intended to be exhaustive or to limit theinvention to the precise forms disclosed, and obviously manymodifications and variations are possible in light of the aboveteaching. The example embodiments, as described above, were chosen anddescribed in order to best explain the principles of the invention andits practical application to thereby enable others skilled in the art tobest utilize the invention in various embodiments and with variousmodifications as are suited to the particular use contemplated. It isintended that the scope of the invention be defined by the claimsappended hereto.

What is claimed as new and desired to be protected by Letters Patent of the United States is:
 1. A device comprising: a bit-to-symbol generator operable to generate a symbol stream comprising a plurality of symbols, the symbol stream being based on a source data stream; and a continuous phase modulator operable to modulate the symbol stream, based on a plurality of modulator code parameters, including an alphabet size M indicating a maximum number of transmission symbols, a modulation index h, a pulse width L, a target pulse reflecting a combination of a raised-cosine pulse and a rectangular pulse, a forward error correction (FEC), a code rate R, and a symbol spacing Δ_(f)T, wherein q_(AV) is a continuous phase modulation phase response of the target pulse as a function of time, wherein q_(RC) is a continuous phase modulation phase response of the raised-cosine pulse as a function of time, wherein q_(RE) is a continuous phase modulation phase response of the rectangular pulse as a function of time, and wherein q_(AV) comprises a weighted average combination of q_(RC) and q_(RE) based on respective weighting factors ∝_(RC) and ∝_(RE), wherein, for a given throughput (bits/sec/Hz), the weighting factor ∝_(RC) is determined to optimize a width of a main lobe for q_(RC) and the weighting factor ∝_(RE) is determined to optimize a level of side lobes for q_(RE).
 2. The device of claim 1, wherein the alphabet size M is 4 symbols and the pulse width is 2, and wherein, for a throughput (in bits/sec/Hz) of 0.5, 0.75, 1.1 or 1.25, the FEC is a (5, 7)_(octal) forward error correction, and, for a throughput (in bits/sec/Hz) of 1.5 or 1.8, the FEC is a (15, 17)_(octal) forward error correction.
 3. The device of claim 2, wherein, for the throughput (in bits/sec/Hz) of 0.5, the modulation index h is 2/5, the code rate R is 1/2, the symbol spacing Δ_(f)T is 2.0, and ∝_(RE)=0.02 and ∝_(RC)=0.98.
 4. The device of claim 2, wherein, for the throughput (in bits/sec/Hz) of 0.75, the modulation index h is 1/3, the code rate R is 1/2, the symbol spacing Δ_(f)T is 1.333, and ∝_(RE)=0.25 and ∝_(RC)=0.75.
 5. The device of claim 2, wherein, for the throughput (in bits/sec/Hz) of 1.1, the modulation index h is 2/7, the code rate R is 2/3, the symbol spacing Δ_(f)T is 1.21, and ∝_(RE)=0.25 and ∝_(RC)=0.75.
 6. The device of claim 2, wherein, for the throughput (in bits/sec/Hz) of 1.25, the modulation index h is 2/7, the code rate R is 2/3, the symbol spacing Δ_(f)T is 1.067, and ∝_(RE)=0.25 and ∝_(RC)=0.75.
 7. The device of claim 2, wherein, for the throughput (in bits/sec/Hz) of 1.5, the modulation index h is 1/4, the code rate R is 4/5, the symbol spacing Δ_(f)T is 1.0667, and ∂_(RE)=0.25 and ∂_(RE)=0.75.
 8. The device of claim 2, wherein, for the throughput (in bits/sec/Hz) of 1.8, the modulation index h is 1/5, the code rate R is 6/7, the symbol spacing Δ_(f)T is 0.974, and ∝_(RE)=0.35 and ∝_(RE)=0.65.
 9. A method comprising: generating, by way of a bit-to-symbol generator, a symbol stream comprising a plurality of symbols, the symbol stream being based on a source data stream; and modulating, by way of a continuous phase modulator, the symbol stream, based on a plurality of modulator code parameters, including an alphabet size M indicating a maximum number of transmission symbols, a modulation index h, a pulse width L, a target pulse reflecting a combination of a raised-cosine pulse and a rectangular pulse, a forward error correction (FEC), a code rate R, and a symbol spacing Δ_(f)T, wherein q_(AV) is a continuous phase modulation phase response of the target pulse as a function of time, wherein q_(RC) is a continuous phase modulation phase response of the raised-cosine pulse as a function of time, wherein q_(RE) is a continuous phase modulation phase response of the rectangular pulse as a function of time, and wherein q_(AV) comprises a weighted average combination of q_(RC) and q_(RE) based on respective weighting factors ∝_(RC) and ∝_(RE), wherein, for a given throughput (bits/sec/Hz), the weighting factor ∝_(RC) is determined to optimize a width of a main lobe for q_(RC) and the weighting factor ∝_(RE) is determined to optimize a level of side lobes for q_(RE).
 10. The method of claim 9, wherein the alphabet size M is 4 symbols and the pulse width is 2, and wherein, for a throughput (in bits/sec/Hz) of 0.5, 0.75, 1.1 or 1.25, the FEC is a (5, 7)_(octal) forward error correction, and, for a throughput (in bits/sec/Hz) of 1.5 or 1.8, the FEC is a (15, 17)_(octal) forward error correction.
 11. The method of claim 10, wherein, for the throughput (in bits/sec/Hz) of 0.5, the modulation index h is 2/5, the code rate R is 1/2, the symbol spacing Δ_(f)T is 2.0, and ∝_(RE)=0.02 and ∝_(RE)=0.98.
 12. The method of claim 10, wherein, for the throughput (in bits/sec/Hz) of 0.75, the modulation index h is 1/3, the code rate R is 1/2, the symbol spacing Δ_(f)T is 1.333, and ∝_(RE)=0.25 and ∝_(RE)=0.75.
 13. The method of claim 10, wherein, for the throughput (in bits/sec/Hz) of 1.1, the modulation index h is 2/7, the code rate R is 2/3, the symbol spacing Δ_(f)T is 1.21, and ∝_(RE)=0.25 and ∝_(RE)=0.75.
 14. The method of claim 10, wherein, for the throughput (in bits/sec/Hz) of 1.25, the modulation index h is 2/7, the code rate R is 2/3, the symbol spacing Δ_(f)T is 1.067, and ∝_(RE)=0.25 and ∝_(RE)=0.75.
 15. The method of claim 10, wherein, for the throughput (in bits/sec/Hz) of 1.5, the modulation index h is 1/4, the code rate R is 4/5, the symbol spacing Δ_(f)T is 1.0667, and ∝_(RE)=0.25 and ∝_(RE)=0.75.
 16. The method of claim 10, wherein, for the throughput (in bits/sec/Hz) of 1.8, the modulation index h is 1/5, the code rate R is 6/7, the symbol spacing Δ_(f)T is 0.974, and ∝_(RE)=0.35 and ∝_(RE)=0.65.
 17. A device comprising: a receiver operable to receive a modulated signal; a demodulator operable to demodulate the modulated signal and generate a demodulated signal, and to generate a symbol stream comprising a plurality of symbols based on the demodulated signal, wherein a modulation scheme reflected by the modulated signal is based on a plurality of modulator code parameters, including an alphabet size M indicating a maximum number of transmission symbols, a modulation index h, a pulse width L, a target pulse reflecting a combination of a raised-cosine pulse and a rectangular pulse, a forward error correction (FEC), a code rate R, and a symbol spacing Δ_(f)T, wherein q_(AV) is a continuous phase modulation phase response of the target pulse as a function of time, wherein q_(RC) is a continuous phase modulation phase response of the raised-cosine pulse as a function of time, wherein q_(RE) is a continuous phase modulation phase response of the rectangular pulse as a function of time, and wherein q_(AV) comprises a weighted average combination of q_(RC) and q_(RE) based on respective weighting factors ∝_(RC) and ∝_(RE), wherein, for a given throughput (bits/sec/Hz), the weighting factor ∝_(RC) is determined to optimize a width of a main lobe for q_(RC) and the weighting factor ∝_(RE) is determined to optimize a level of side lobes for q_(RE).
 18. The device of claim 17, wherein the alphabet size M is 4 symbols and the pulse width is 2, and wherein, for a throughput (in bits/sec/Hz) of 0.5, 0.75, 1.1 or 1.25, the FEC is a (5, 7)_(octal) forward error correction, and for a throughput (in bits/sec/Hz) of 1.5 or 1.8 the FEC is a (15, 17)_(octal) forward error correction.
 19. The device of claim 18, wherein, for the throughput (in bits/sec/Hz) of 0.5, the modulation index h is 2/5, the code rate R is 1/2, the symbol spacing Δ_(f)T is 2.0, and ∝_(RE)=0.02 and ∝_(RE)=0.98.
 20. The device of claim 18, wherein, for the throughput (in bits/sec/Hz) of 0.75, the modulation index h is 1/3, the code rate R is 1/2, the symbol spacing Δ_(f)T is 1.333, and ∝_(RE)=0.25 and ∝_(RE)=0.75.
 21. The device of claim 18, wherein, for the throughput (in bits/sec/Hz) of 1.1, the modulation index h is 2/7, the code rate R is 2/3, the symbol spacing Δ_(f)T is 1.21, and ∝_(RE)=0.25 and ∝_(RE)=0.75.
 22. The device of claim 18, wherein, for the throughput (in bits/sec/Hz) of 1.25, the modulation index h is 2/7, the code rate R is 2/3, the symbol spacing Δ_(f)T is 1.067, and ∝_(RE)=0.25 and ∝_(RE)=0.75.
 23. The device of claim 18, wherein, for the throughput (in bits/sec/Hz) of 1.5, the modulation index h is 1/4, the code rate R is 4/5, the symbol spacing Δ_(f)T is 1.0667, and ∝_(RE)=0.25 and ∝_(RE)=0.75.
 24. The device of claim 18, wherein, for the throughput (in bits/sec/Hz) of 1.8, the modulation index h is 1/5, the code rate R is 6/7, the symbol spacing Δ_(f)T is 0.974, and ∝_(RE)=0.35 and ∝_(RE)=0.65.
 25. A method comprising: receiving a modulated signal; demodulating by way of a demodulator, the modulated signal and generating a demodulated signal; and generating a symbol stream comprising a plurality of symbols, the symbol stream being based on the demodulated signal, wherein a modulation scheme reflected by the modulated signal is based on a plurality of modulator code parameters, including an alphabet size M indicating a maximum number of transmission symbols, a modulation index h, a pulse width L, a target pulse reflecting a combination of a raised-cosine pulse and a rectangular pulse, a forward error correction (FEC), a code rate R, and a symbol spacing Δ_(f)T, wherein q_(AV) is a continuous phase modulation phase response of the target pulse as a function of time, wherein q_(RC) is a continuous phase modulation phase response of the raised-cosine pulse as a function of time, wherein q_(RE) is a continuous phase modulation phase response of the rectangular pulse as a function of time, and wherein q_(AV) comprises a weighted average combination of q_(RC) and q_(RE) based on respective weighting factors ∝_(RC) and ∝_(RE), wherein, for a given throughput (bits/sec/Hz), the weighting factor ∝_(RC) is determined to optimize a width of a main lobe for q_(RC) and the weighting factor ∝_(RE) is determined to optimize a level of side lobes for q_(RE).
 26. The method of claim 25, wherein the alphabet size M is 4 symbols and the pulse width is 2, and wherein, for a throughput (in bits/sec/Hz) of 0.5, 0.75, 1.1 or 1.25, the FEC is a (5, 7)_(octal) forward error correction, and for a throughput (in bits/sec/Hz) of 1.5 or 1.8 the FEC is a (15, 17)_(octal) forward error correction.
 27. The method of claim 26, wherein, for the throughput (in bits/sec/Hz) of 0.5, the modulation index h is 2/5, the code rate R is 1/2, the symbol spacing Δ_(f)T is 2.0, and ∝_(RE)=0.02 and ∝_(RC)=0.98.
 28. The method of claim 26, wherein, for the throughput (in bits/sec/Hz) of 0.75, the modulation index h is 1/3, the code rate R is 1/2, the symbol spacing Δ_(f)T is 1.333, and ∝_(RE)=0.25 and ∝_(RC)=0.75.
 29. The method of claim 26, wherein, for the throughput (in bits/sec/Hz) of 1.1, the modulation index h is 2/7, the code rate R is 2/3, the symbol spacing Δ_(f)T is 1.21, and ∝_(RE)=0.25 and ∝_(RC)=0.75.
 30. The method of claim 26, wherein, for the throughput (in bits/sec/Hz) of 1.25, the modulation index h is 2/7, the code rate R is 2/3, the symbol spacing Δ_(f)T is 1.067, and ∝_(RE)=0.25 and ∝_(RC)=0.75.
 31. The method of claim 26, wherein, for the throughput (in bits/sec/Hz) of 1.5, the modulation index h is 1/4, the code rate R is 4/5, the symbol spacing Δ_(f)T is 1.0667, and ∝_(RE)=0.25 and ∝_(RC)=0.75.
 32. The method of claim 26, wherein, for the throughput (in bits/sec/Hz) of 1.8, the modulation index h is 1/5, the code rate R is 6/7, the symbol spacing Δ_(f)T is 0.974, and ∝_(RE)=0.35 and ∝_(RC)=0.65. 